Answer: [tex]f(x) = \left \{ {{x + 3---->; x }\leq 2 \atop {-x+7---->; x}\geq2 } \right.[/tex]
Step-by-step explanation:
Left line:
slope (m) = 1 and y - intercept (b) = 3
equation in slope-intercept (y = mx + b) format is: y = x + 3
this line exists only when x ≤ 2
Right line:
a point on the line = (2, 5) and slope (m) = -1
equation in point-slope [y - y₁ = m(x - x₁)] format is: y - 5 = -(x - 2)
convert that to slope-intercept format: y = -x + 2 + 5 ⇒ y = -x + 7
this line only exists when x ≥ 2
[tex]f(x) = \left \{ {{x + 3---->; x }\leq 2 \atop {-x+7---->; x}\geq2 } \right.[/tex]
